Direct Perturbation Method for Reanalysis of Matrix Singular Value Decomposition
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摘要: 矩阵奇异值分解的摄动重分析技术具有广泛的应用前景,作者继在文[2]中提出了一种间接摄动分析方法之后,在本文中又进一步提出了直接摄动法,建立了一般实矩阵的非重奇异值及其左、古奇异向量的二阶摄动计算公式.这可满足大多数实际应用问题的一般需要.文中以算例说明了直接摄动法的有效性.Abstract: The perturbational reanalysis technique of matrix singular value decomposition isapplicable to many theoretical and practical problems in mathematics,mechanics,control theory,engineering,etc..An indirect perturbation method has previously beenproposed by,the author in this journal,and now the direct perturbation method hasalso been presented in this paper.The second-order perturbation results of nonrepeated singular values and the corresponding left and right singular vectors areobtained.The results can meet the general needs of most problems of various practicalapplications.A numerical example is presented to demonstrate the effectiveness of thedirect perturbation method.
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Key words:
- matrix algebra /
- singular value decomposition /
- reanalysis /
- perturbation method
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[1] V.C.Klema and A.J.Laub,The singular value decomposition:its computation and some applications,IEEE Trans.on Antontcttic Control.AC-25(1980),164-]76. [2] 吕振华、冯振东,矩阵奇异值分解问题重分析的摄动法,应用数学和力学,12(1991),705-715. [3] 胡海昌,《多自由度结构固有振动理论》,科学出版社,北京(1987). [4] 吕振华,线性和二次广义特征值问题的矩阵摄动法新探及汽车动力传动系扭振分析方法和控制措施论析,吉林工业大学博士学位论文,(1990). [5] J.R.Newsom and V.Mukhopadhyay,The use of singular value gradients and optimization techniques to design robust controllers for multiloop systems,AIAA Paper,83-2191(1983). [6] V.Mukhopadhyay and J.R.Newsom,Application of matrix singular value properties for evaluating gain and phase margins of multiloop systems,.AIAA Paper,82-1574(1982). [7] A.S.Deif,Adrancccf Matrix Theory for Scientists and Engineers,Abacus Press,Tun-bridge Wells &London(1982). -
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